The broad, long-term objectives of this research are the developments of semiparametric regression models and associated inferential and computational methods for the analysis of censored failure time data com- monly encountered in medical studies. The specific aims of the extension period include:1) to assess the predictive accuracy of clinical and genetic variables in predicting time to disease occurrence or death and to quantify the impact of genetic mutations and environmental exposures on the population over time; 2) to stu- dy a broad class of mixture cure models that combines a binary regression model for the cure probability with a generalized Cox model for the failure times of the uncured individuals; 3) to construct kernel-based es- timation methods for outcome-dependent two-stage designs, such as case-cohort and nested case-control studies; 4) to pursue variable selection strategies for generalized Cox models and accelerated failure time models; 5) to extend the Cox proportional hazards model to accommodate nonproportional hazards structures by allowing the regression coefficients to vary over time or to change from one value to another at a certain time point; 6) to explore empirical likelihood methods for utilizing auxiliary baseline covariate infor- mation to improve the efficiency of treatment comparisons in randomized clinical trials; and 7) to study a broad class of semiparametric regression models for spatially correlated failure time data. All these aims are built on the observations and ideas that have been generated during the MERIT award period and address the most timely and important issues in medical research. In each specific aim, valid and efficient statistical methods will be constructed and their theoretical properties be rigorously established. Efficient and reliable numerical algorithms will be devised to implement the corresponding inference procedures. The performance of the numerical and inferential procedures will be assessed through extensive simulation studies. Applica- tions to a variety of clinical, epidemiological and genetic studies will be provided. User-friendly, open-source software will developed and disseminated. This research will yield novel and powerful statistical and commputational tools that can be readily used by medical investigators.